I would use v2.16, there is an entry for that specific board. I'm starting to think that the v3 should actually be called something else because it seems only support a couple newer boards. You may have to patch it to work (the patch if needed should be provided in a zip file under the documents tab for your processor on the atmel website).

As aarcov suggests, sam-ba v3 is a red herring - the only thing it appears to provide SAM4E users is another frustrating couple of hours getting nowhere.

sam-ba v2.16 is what you want. It seems there used to be a patch for v2.12 to support SAM4E but that's not required anymore for v2.16.

v2.16 comes with a GUI, so use that first. When it launches, select "at91sam4e16-ek" for the SAM4E16E. Be sure to check "Customise lowlevel" and set the options exactly as your board is configured. Click connect, select the "Flash" tab, put your bin file in "Send File Name", and click "Send File". Finally, select the "Boot from Flash" script and execute that. Next time you reset the MCU, it will run your firmware.